Here is the full list of all 20 Spellcaster University achievements.
Achieve a prestige of 100.
Have at least 50 students.
Have at least 10 teachers in your school.
Have 5 dragons of different colors.
Finish a level with all three objectives completed.
Achieve a reputation with the orcs of 100.
Train an archimage.
Having 5 different classes.
Have 5 different kitchen utensils.
Use the power of the guidance counsellor to change a student's future.
Discover if the turtle is a male or a female.
Have a reputation of -100 with the inquisition.
To own 5000 gold pieces.
Slay an orc.
Pay to draw 10 Shadow cards in the same game.
Train at least 10 librarians during the same campaign.
Win a campaign.
Win a campaign in difficult mode.
Achieve a reputation with the king of 100.
Start Spellcaster University on the day of the Beltane festival.